The properties of polycrystalline materials are determined by the properties of the crystallites that form the material and the boundaries between the crystallites. Crystallites may also be referred to as grains, particles or simply crystals. The size of the crystallites in a polycrystalline material has significant effects on many of its properties, such as thermal, mechanical, electrical, magnetic and chemical properties. For instance, the mechanical strength of polycrystalline metals and alloys is strongly dependent on the grain size. This is, in part, due to the fact that deformation of metals is caused by the motion of dislocations and other defects under loading stress and different crystallographic orientations and the boundaries between adjacent grains serve as barriers to the motion of such dislocations and other defects. A metal with finer grains has more boundaries to impede dislocation motion and, therefore, has higher mechanical strength. Particle size can also affect the behavior of pharmaceuticals in many ways, such as dissolubility, bioactivity, flow properties and stability.
Consequently, it is important to measure crystallite size in order to determine or predict the properties of a polycrystalline material. Crystallite size can be measured by many techniques, such as by optical microscopy or electron microscopy techniques on polished and etched surfaces. However, both microscopy techniques require special sample preparation and can only observe the sample surface. X-ray diffraction has been used for crystallite size measurement for over ninety years since X-rays can penetrate a sample and measure crystallite size over the entire volume of the sample, thereby allowing the overall statistics of the crystallite size to be calculated.
The conventional method for determining particle size with X-ray diffraction measurements is based on diffraction peak broadening or diffraction (2θ) profile analysis. When crystallites in a sample are less than approximately 100 nm in size, appreciable broadening in the x-ray diffraction lines measured from that sample will occur and can be used to estimate the average crystallite size. Where the crystallites are stress-free, the size can be estimated from a single diffraction peak; however, where stress may be present, several diffraction peaks may have to be analyzed. The extent of the broadening is described by the measured value B, which is the full width at half maximum intensity of the peak.
After the value of B (in radians) is corrected for instrumental contribution to the broadening, it can be substituted into Scherer's equation for the particle size D:
  D  ≈            0.9      ⁢      λ              B      ⁢                          ⁢      cos      ⁢                          ⁢      Θ      
where λ is the X-ray wavelength and Θ is the diffraction angle.
Although X-ray diffraction line broadening is clearly present when the particle size is smaller than 100 nm, in practice, the Scherer equation can adequately determine the average size of crystallites smaller than 30 nm when the broadening is significant enough to be resolved from instrumental broadening. However, there are many situations where it would be desirable to measure particle size where the particle size is considerably larger than 100 nm. For instance, the particle sizes in pharmaceutical systems are typically in the range of a few micrometers to millimeters. In these systems, conventional methods of particle size analysis by x-ray diffraction are not always suitable.